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Theorem bnj170 29862
Description: -manipulation. (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (Proof shortened by Andrew Salmon, 14-Jun-2011.) (New usage is discouraged.)
Assertion
Ref Expression
bnj170 ((𝜑𝜓𝜒) ↔ ((𝜓𝜒) ∧ 𝜑))

Proof of Theorem bnj170
StepHypRef Expression
1 3anrot 1035 . 2 ((𝜑𝜓𝜒) ↔ (𝜓𝜒𝜑))
2 df-3an 1032 . 2 ((𝜓𝜒𝜑) ↔ ((𝜓𝜒) ∧ 𝜑))
31, 2bitri 262 1 ((𝜑𝜓𝜒) ↔ ((𝜓𝜒) ∧ 𝜑))
Colors of variables: wff setvar class
Syntax hints:  wb 194  wa 382  w3a 1030
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 195  df-an 384  df-3an 1032
This theorem is referenced by:  bnj543  30062  bnj605  30076  bnj594  30081  bnj607  30085  bnj908  30100  bnj1173  30169
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